The issue with Skarner's new design...

...seems to be a simple logical one.

So his identity is now tied to these secondary objectives on the map, encouraging players to contest them and fight in the jungle over controlling them. You can't ever give the enemy team serious benefits for having control of them or else Skarner becomes a liability for his team, so the only benefit they can have is to deprive Skarner of the buff he gets. In order for them to be worth contesting at all then, they have to make Skarner very, very strong when he is in the aoe. That way he will want to utilize them, and enemies will want to limit his reign of terror.

Here's the thing though. Numbers on the stat buffs and everything aside, the lockout timers aren't long enough to make fighting over them worthwhile. For the enemy, it is DEFINITELY better to just wait for skarner to go away before capturing them, and even if captured, Skarner is only delayed a measly 15 seconds. The value of an objective is heavily affected by how long you can deprive the enemy of it, like with dragon. I think the capture lockout time needs to be extended to AT LEAST 2 minutes. Maybe 3 minutes. That way you have plenty of time to make plays one way or the other while a zone is under your control. This is as essential for skarner to utilize them effectively as it is for the enemy to shut him down. Since the lockout will be longer, you could consider adding more gold to the reward for enemies capturing the spires. Maybe 50 gold, a little more than scuttle crab. For obvious reasons, both sides should start with their jungle spires captured and the neutral ones should stay locked out for the first two minutes of the game. No sense in giving out free starting health potions.

Second, the aoe on the Spires is WAY too small. You might think that the small aoe is a good trade off, but think about that for a second. If Skarner's power is tied to an absurdly small space, then the power it grants him must be proportionally absurd in order to be incentivized. Extending out the range to reflect quadrants of the map allows you to balance out the scale of his strengths while increasing the scope of their application. Unless you literally intend for Skarner to just stand on these things and fight anyone dumb enough to approach him, which is a terrible idea because junglers have important things to do, like contribute to their teams. Extending the range of the aoe not only allows skarner to actually apply his strength to controlling the map, but also gives the spires a wide enough impact to encourage early teamfights and skirmishes over them.

Specifically, I would alter the locations and ranges of the spires to encompass 'From outside the base to in front of the inner turret in the mid and respective side lane' for the ones in jungle, and 'between the outer towers and surrounding the respective neutral objective, extending into jungle entrances' for the dragon and baron spires. This wider area of control allows spires to be a bigger part of skarner's gameplay, and a bigger part of rewarding or punishing him. Some overlap on the aoe is ok, since Skarner's playstyle largely revolves around chasing enemies who don't want to fight him. In fact the aoe for either side SHOULD overlap in mid lane, since Skarner should be focusing on capturing the areas he wants to apply pressure to, instead of trying to hold down the whole map. Plus map control is an important part of responsible mid laning. No bonuses within the walls of either base though, since if he is in your base, he is winning hard enough, and if you are fighting him in his base, he shouldn't get free buffs in a place you can't really contest to stop your push with.

Third, if you want Skarner to be about Map Control, and you want to make his passive stat boosts both fair and rewarding, while keeping his design balanced, they NEED to come off of his ultimate/stun. It does no good for enemies to capture his spires if he can just get the same buffs by beating their faces in, which rewards him with the ability to beat faces in even better. Skarner needs to be relatively vulnerable if he isn't holding his spires, allowing enemies to punish and shut him down, and that will just never be meaningful if he can proc the same buff using abilities he was going to use to do his job anyway.

Ultimately it still might be a doomed design, but it would definitely be more workable with these changes I think.

TL;DR:
1) Increase lockout timer on spire capture to 2-3 minutes. 2) Increase spire aoe to encompass regions of the map, a bit of overlap is ok. 3) Remove the Spire Buffs from Skarner's kit, he shouldn't need them if he is utilizing his spires, and he shouldn't get them if he isn't. 4) I shouldn't even have to say this, but the numbers on his Spire Buffs are probably also in need of tuning. They might be a bit over the top, though the mana is probably fine. 5) With the increased lockout timer and wider zone of control, you could increase the gold reward for enemy capture of spires to reflect a mini
neutral objective. I'd say about 50 gold, split evenly between everyone participating in the capture. Teams start with their respective jungle spires captured and neutral objective spires stay locked out from capture for the first two minutes of the game.